1. Field of Invention
The present invention relates to an improved method for calculating the pressure of fluid contained in a sedimentary rock which has been naturally compacted under the influence of gravity. A more accurate calculated pore pressure profile at various depth ranges produced according to the method of this invention produces valuable geological information useful in the hydrocarbon recovery industry.
2. Background
Pore fluid pressure is the major factor affecting the planning and drilling of an oil well. The borehole fluid hydrostatic pressure must be greater than the formation pore fluid pressure if one is to avoid the possibly catastrophic risk of blowout. Likewise, the borehole fluid circulating pressure must be less than fracture propagation pressure if one is to avoid the risk of lost circulation. Several expensive casing strings are usually required so that an oil well can be drilled within these two pore fluid pressure and fracture propagation pressure limits. The present invention thus enhances the safety of oil or gas well drilling operations, and also reduces the overall cost of hydrocarbon recovery by providing more reliable information to a drilling operator and thus avoiding complicated correction operations.
Because of its critical relationship to drilling operations, there are numerous techniques for calculating pore fluid pressure. All known petrophysical prior art methods calculate pore fluid pressure indirectly based upon measured rock properties, e.g., rock density or drilling rate of penetration. Most of these methods follow a calibration procedure which is not based on mechanical or physical information. Instead, these calibration procedures are generally based upon an observed empirical relationship between a measured physical parameter and a "normal" or hydrostatic compaction trend. The "normal" trend line is the average value of the measured parameter which changes as a function of depth. The change in the measured parameter according to these prior art techniques is thus related to a change in compaction of the sedimentary rock.
Sedimentary rocks are compacted by the stress applied to their grain matrix framework, which is not solely function of depth. When fluid pressure is approximately hydrostatic and the overburden is gradually increasing, both depth and stress are increasing. Under these conditions, depth behaves as a pseudo-stress variable. However, when pore pressure is elevated, effective stress and overburden gradients can be either increasing or decreasing and depth is not a pseudo-stress variable. Most of the prior art methods for determining pore fluid pressure use depth as a pseudo-stress variable in both "normal" and "excess" pressured intervals which results in significant pore pressure calculation errors.
Another significant failing of prior art pore pressure calculation techniques is attributable to their basic formulation. According to prior art techniques, pore pressure (P) is calculated as a sum of "normal" hydrostatic fluid pressure (Pn) which is inferred from compaction-depth trend, plus a differential or "excess" fluid pressure (.DELTA.P) which is related to a measured difference from the "normal" trend. The equation expressing this relationship is: EQU P=Pn+.DELTA.P (1)
Equation 1 is a physically incorrect mathematical formulation. In fact, Pascal's Principle requires that all of the fluids in a given local pore space or container be at the same pressure. Since the "excess" pressure term (.DELTA.P) does not exist in nature, there is no way it can be physically related to a measured parameter. Calibrating a measured physical parameter to a quantity which does not exist (.DELTA.P) is not reasonably sound.
The "normal compaction" vs depth trend line methods give the drilling operator a false sense of confidence based entirely upon the hydrostatic (Pn) calibration interval, wherein depth is a pseudo-stress variable. Pascal's Principle is not violated in the upper hydrostatic (Pn) interval because .DELTA.P=0 and P=Pn. Unfortunately, this sense of confidence gained in the (Pn) calibration interval is then transferred to the associated empirical "excess" pressured (.DELTA.P) calibration where two entirely different conditions apply.
In the "excess pressured" interval, depth is not a pseudo-stress variable. Also, the change in the measured physical parameter, such as density, resistivity, or rate of penetration, is related according to this prior art technique to the positive (.DELTA.P) term of Equation 1, which violates Pascal's Principle. Apparent success of pore pressure predictions derived from these methods below the base of the hydrostatically compacted interval may be due to a coincidence between pressure and depth which is peculiar to a given area or depth range. Any correspondence between calculated and observed pore pressures cannot be attributed to a physical relationship between the measured parameter and the excess fluid pressure, however, because such a relationship does not physically exist.
Lacking a physical cause-effect relationship, these prior art methods have been judged on a raw observed pressure vs. hydrostatic fluid pressure (Pn) trend basis. The (.DELTA.P) calibration correlates the difference between the observed measurement and the projected (Pn) normal compaction trend. There is no data to support the (Pn) projection below the top of the overpressured (.DELTA.P) zone because known pressure (P) is above (Pn). Consequently, all these methods include depth below the base of (Pn) as a contributing calibration factor. To make these "calibrations" work, similar depth-pore pressure profiles are taken within a given study area. What is presumed to be pore pressure prediction accuracy using these methods is actually a raw vs an averaged form of the same pressure data within a given area. The scatter of data about its own average trend is more commonly known as measurement precision. A narrow scatter within a given study area, such as reported in a 1965 article by Hottman et al., actually also means that depth-pore pressure profiles are similar within the area. In that case, the only measurement that is needed to successfully predict pore pressure is the measured depth to the top of the overpressured zone. A paper published that same year by Matthews et al shows both positively and negatively curving correlations of (.DELTA.P) to resistivity in different study areas and depth ranges. If there was a direct correlation between resistivity and pore pressure, one would expect one relationship or the other, but not both. The dozens of pore pressure methods in practice today which follow the P=Pn+.DELTA.P formulation violate a law of physics in their fluid pressure calibration and are flawed since they are not based on valid theories.
U.S. Pat. No. 4,833,914 to Rasmus is an example of a P=Pn+.DELTA.P method which violates Pascal's Principle. Rasmus volumetrically subdivides total rock porosity into overpressured porosity, effective porosity, and water porosity. A response equation solver then uses these terms to solve for pore pressure. As all fluid molecules are free to exchange position with each other through Brownian movement, there is no boundary between these artificially calculated pore volumes and no natural way to define them. The overpressured pore volume used by Rasmus is also a (.DELTA.P) term which exists in the same total pore space as "normally pressured" pore volume, which further violates Pascal's Principle. The method uses complicated statistics to converge on these artificially calculated, physically non-existent pore volume terms. This patent discloses pressure results being calculated in shales only from the "overpressured porosity" term. Although this calibration technique is performed statistically with a computer, it has the same physical shortcomings of the methods described in the previous paragraph.
U.S. Pat. No. 5,081,612 to Scott et al discloses a method for determining formation pore pressure from remotely sensed seismic data. This particular method and the prior art methods cited in this patent depend upon a hydrostatically compacted reference velocity profile. Referring back to Equation 1, this profile is essentially an observed or inferred curved (Pn) velocity gradient. The Scott et al pore pressure gradient technique applies to only one lithology, which is common to most of the prior art methods using a P=Pn+.DELTA.P formulation. Pore pressures are calculated with respect to the reference velocity gradient, which again is a violation of Pascal's Principle.
A 1990 article by Haas presented a seismic data pore pressure method which accounts for the difference in formation velocity which is a function of lithology and not pore pressure. These lithologic changes are "normalized" out by either addition or subtraction to make a smooth (Pn) velocity trend. After normalization, a velocity overlay is developed which empirically relates P=Pn+.DELTA.P by using lithology normalized velocity as the measured parameter. To operate properly, this Haas method would require all lithologies to compact in the same manner after normalization. Different lithologies did not compact similarly before their transit time offset normalization, and there is no logical basis to presume that they would compact similarly after offset normalization. The Haas procedure does not make rock compactional sense, and results derived therefrom should be suspect.
There are at least three prior art methods for determining pore fluid pressure from petrophysical measurements which are based upon the effective stress law, which was first elucidated by Terzaghi in 1923 through compactional studies of marine sediments: EQU P=S-.sigma..sub.v ( 2)
This relationship states that the fluid pressure in the pore space (P) can be calculated as the difference between the total overburden load (S) and the load borne by the sediment grain-grain contacts (.sigma..sub.v). In the science of rock and soil mechanics, this .sigma..sub.v term is known as the effective stress. Effective stress law is not widely used today for pore pressure prediction for various reasons, including the absence of an effective .sigma..sub.v calibration technique.
Effective stress was ignored by most geologic compaction studies, which instead evaluated geologic compaction as depth - porosity functions. Overburden gradients which differ considerably from place to place were assumed to be equal or uniformly varying. Although pore pressure was mentioned as a possible explanation for porosity differences, it was not subtracted from the total overburden load (S) to calculate effective stress. The mechanical effective stress explanation for the differences in porosity vs depth trends were thus ignored by geologists. The differences between porosity vs depth compaction curves were instead attributed to geologic factors such as geologic age and temperature. Articles by Maxwell published in 1964, and by Schmoker et al in 1988 and 1989, evidence this explanation.
A 1972 article by Baldwin et al unified the compaction of shales worldwide through use of a power law solidity vs depth relationship. These researchers re-cast the then-standard shale porosity vs depth curves, noting that each of the compaction curves from 14 worldwide basins fell within 2% of the Baldwin et al worldwide average power law solidity vs depth relationship. These researchers then substituted effective stress (.sigma..sub.v) for depth in a power law equation of the same form: EQU .sigma..sub.v =.sigma..sub.max (Solidity).sup..alpha.+1 ( 3)
In this equation, the .sigma..sub.max term is the power law intercept of the compaction curve with the 100% solidity axis. .sigma..sub.max is the effective stress that will cause complete compaction of the sedimentary particle mixture. .alpha.+1 is the slope of the power law compaction function for that granular material. This seemingly simple mathematical substitution transformed the Baldwin et al unified depth (pseudo-stress) empirical compaction function into a mechanically sound stress-strain relationship. The critical difference between this and all other compaction functions is that effective stress is the load applied to the sedimentary rock grain matrix framework. Solidity is a linear function of the compactional strain experienced by that rock grain matrix framework. Calibration using this equation represents a sound cause-effect relationship based on valid mechanical theories. However, Baldwin et al made no attempt to calculate pore pressure using this approach. The accompanying discussion of sandstone compaction curves in the Baldwin et al article indicated that sandstone compaction was apparently not governed by power law functions. The observed wide variance between sandstone compaction curves between different basins apparently suggested to them that no unified sandstone compaction function was possible.
A 1987 article by Holbrook et al and U.S. Pat. No. 4,981,037 applied the effective stress law for pore pressure prediction using a power law effective stress compaction function. The initial .sigma..sub.max and, .alpha.+1 constants used were expressed in the Baldwin et al article. The method was highly successful at predicting pore pressures in mid-shelf and off-shelf Gulf Coast sandstone-shale sequences. However, very deep highly sand prone wells forced a change of the effective stress constants .sigma..sub.max and .alpha. to higher values than suggested by Baldwin et al. The revised constants include the effects of pore pressure and are based upon calculated stress rather than pseudo-stress. The revised constants are more accurate and cover a broader depth and stress range than the Baldwin et al constants.
1989 and 1992 articles by Alixant also disclose the use of the effective stress law for pore pressure prediction. However, Alixant used a single laboratory derived compaction function, which he applied to shales only. In field testing, the compaction constant could not accurately cover the range of shale solidities. This method requires considerable changes in unrelated non-physical constants to match observed pore pressure data within a given local area. It is known, however, that strain hardening changes the compaction function of a rock. A constant laboratory compaction function can calculate stress from strain accurately only where the constant coincidentally matches the changing compaction function.
Another 1989 article by Bryant also disclosed an attempt to use the effective stress law for pore pressure prediction. Bryant used an average exponential function to calculate overburden as a function of depth rather than data from the well. His results were inaccurate partially because of this average exponential function, and partially because he used the same compaction function for sandstones and shales. Bryant's methods in not in common use today, possibly due to these large inaccuracies.
Holbrook extended the effective stress concept to the prediction of vertical fracture propagation pressure in a 1989 article. This approach was at least 4 times more accurate than prior art fracture pressure methods. Leakoff tests calibrated using this effective stress method all fell at or below the calculated overburden for that depth. Kehle noted in a 1964 article that all his observed onshore leakoff tests fell below the calculated overburden. However, neither the Kehle nor Holbrook articles used this observation as a feedback mechanism to improve the calculation of formation pore fluid pressure.
The disadvantages of the prior art are overcome by the present invention, and improved and techniques are hereinafter disclosed for more accurately calculating pore pressure of sedimentary rock which has been naturally compacted under the influence of gravity. The techniques of the present invention provide more meaningful pore pressure profiles which are useful in the hydrocarbon recovery industry.